<html>
  <head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
    <title>des2tf</title>
  </head>
  <body bgcolor="#FFFFFF">
    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>des2tf</b> -  descriptor to transfer function conversion</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[S]=des2tf(sl)  </tt>
      </dd>
      <dd>
        <tt>[Bfs,Bis,chis]=des2tf(sl)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>sl</b>
        </tt>: list (linear system in descriptor form)</li>
      <li>
        <tt>
          <b>Bfs, Bis</b>
        </tt>: two polynomial matrices</li>
      <li>
        <tt>
          <b>chis</b>
        </tt>: polynomial</li>
      <li>
        <tt>
          <b>S</b>
        </tt>: rational matrix</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    Given the linear system in descriptor form i.e.
    <tt>
        <b>Sl=list('des',A,B,C,D,E)</b>
      </tt>, <tt>
        <b>des2tf</b>
      </tt> converts <tt>
        <b>sl</b>
      </tt> into
    its transfer function representation:</p>
    <pre>

S=C*(s*E-A)^(-1)*B+D
   
    </pre>
    <p>
    Called with 3 outputs arguments <tt>
        <b>des2tf</b>
      </tt> returns
    <tt>
        <b>Bfs</b>
      </tt> and <tt>
        <b>Bis</b>
      </tt> two polynomial matrices, and <tt>
        <b>chis</b>
      </tt>
    polynomial such that:</p>
    <pre>

S=Bfs/chis - Bis
   
    </pre>
    <p>
      <tt>
        <b>chis</b>
      </tt> is the determinant of <tt>
        <b>(s*E-A)</b>
      </tt> (up to a xcative constant);</p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

s=poly(0,'s');
G=[1/(s+1),s;1+s^2,3*s^3];
Descrip=tf2des(G);Tf1=des2tf(Descrip)
Descrip2=tf2des(G,"withD");Tf2=des2tf(Descrip2)
[A,B,C,D,E]=Descrip2(2:6);Tf3=C*inv(s*E-A)*B+D
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="../linear/glever.htm">
        <tt>
          <b>glever</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../polynomials/pol2des.htm">
        <tt>
          <b>pol2des</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../robust/tf2des.htm">
        <tt>
          <b>tf2des</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="ss2tf.htm">
        <tt>
          <b>ss2tf</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../robust/des2ss.htm">
        <tt>
          <b>des2ss</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="../linear/rowshuff.htm">
        <tt>
          <b>rowshuff</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
    <h3>
      <font color="blue">Author</font>
    </h3>
    <p>F. D.  </p>
  </body>
</html>
